Lasing in Two-Dimensional Tin Perovskites

Two-dimensional (2D) perovskites have been proposed as materials capable of improving the stability and surpassing the radiative recombination efficiency of three-dimensional perovskites. However, their luminescent properties have often fallen short of what has been expected. In fact, despite attracting considerable attention for photonic applications during the last two decades, lasing in 2D perovskites remains unclear and under debate. Here, we were able to improve the optical gain properties of 2D perovskite and achieve optically pumped lasing. We show that the choice of the spacer cation affects the defectivity and photostability of the perovskite, which in turn influences its optical gain. Based on our synthetic strategy, we obtain PEA2SnI4 films with high crystallinity and favorable optical properties, resulting in amplified spontaneous emission (ASE) with a low threshold (30 μJ/cm2), a high optical gain above 4000 cm–1 at 77 K, and ASE operation up to room temperature.

treated under oxygen plasma. The hot solution (100 °C) was dropped on the glass substrate and immediately spin coated at 5000 rpm for 30s. During the process, the lid of the spin coater was left open to allow a faster evaporation of the solvent. The films were annealed at 100 °C for 15 min. Solution preparation and film processing were performed in a nitrogen-filled glovebox.

Structural and morphological characterization.
Perovskite thin films were characterized with X-ray diffraction (XRD) using a BRUKER D8 ADVANCE with Bragg-Brentano geometry, Cu Kα radiation (λ = 1.54056 Å), step increment of 0.02° and 1 s of acquisition time. For temperature-dependent XRD measurements, the sample was placed in a MTC-LOWTEMP chamber, where the temperature is controlled through an AlCr heater and a cold probe flushed with liquid nitrogen. The sample was cooled at the rate of 10 °C/min, with a thermalization of 5 minutes before starting the data acquisition at each selected temperature. The film thickness was measured with a surface profiler Dektak 150 (Veeco) while the film morphology was characterized with a scanning electron microscope (SEM) MIRA3, TESCAN (in this case, the films were prepared on top of conductive ITO/glass to avoid charging effects during the image acquisition).

Spectroscopic characterization.
The samples were either encapsulated or kept in vacuum during the measurements to prevent oxidation. Steady state absorption spectra were measured on perovskite thin films deposited on glass with a UV/VIS/NIR spectrophotometer Lambda 1050, Perkin Elmer. Room temperature photoluminescence experiments were performed in a NanoLog (Horiba Jobin Yvon).
Temperature-dependent experiments were performed with a Linkam Stage HFS350EV-PB4 using a nitrogen-cooled cold finger.

Photothermal Deflection Spectroscopy
In Photothermal Deflection Spectroscopy (PDS) the absorption spectrum of a thin film can be obtained by monitoring the change of refractive index of the medium surrounding its surface.
The sample is submerged in Tetradecafluorohexane and it is illuminated by a monochromatic light provided by a SuperK Extreme supercontinuum laser, coupled with a SuperK SELECT acousto-optic tunable filter (NKT Photonics). The thermal relaxation of the photogenerated carriers creates a thermal gradient in the portion of liquid around the sample's surface. This, in turn, establishes a refractive index gradient (mirage effect) that deflects a He-Ne laser (JDSU)) aligned parallel and in close proximity to the sample's surface. The steering of the He-Ne laser is measured by a quadrant detector (PDQ80A, Thorlabs). The absorption coefficient, at each wavelength, is proportional to the amplitude of the deflection signal, granting high sensitivity scatter-free detection. The excitation light is modulated by a chopper (4 Hz) to enable lock-in detection (SR830), and by changing its wavelength we retrieve the full absorption spectrum (after normalizing for the power spectrum of the laser). Long-pass filters are used to prevent leakage straylight.

ASE & VSL measurements
The samples were excited with a pulsed 532 nm green laser (Innolas Picolo 2nd harmonic), having a pulse duration of 800 ps and a repetition rate of 1 kHz. The excitation fluence was controlled with a filter wheel. The emission was detected with a fiber coupled Maya 1000 spectrometer (1 nm resolution). The pump radiation was filtered by using a 550 nm long-pass filter. For the ASE variable pump intensity measurements, the beam was focused using a 10 cm spherical lens. While in the case of the VSL measurement, a cylindrical lens (f = 100 mm) focused the laser beam on a 1 mm slit, resulting in a stripe-shaped beam of adjustable length, that was then imaged on the sample with a biconvex lens (f = 50 mm). The full details of the VSL procedure were previously reported. 26

Ellipsometry
The optical constants, namely the refractive index (n) and the extinction coefficient (k), of PEA 2 SnI 4 were measured using an ellipsometer (J.A. Woollam M-2000 Ellipsometer). The sample was spin coated on a glass substrate and the ellipsometry spectra were measured in air and in reflection mode. Ellipsometry data were collected in a wavelength range of 370 -1696 nm, and at angles of incidence of 50-60º, with steps of 5º. The optical constants were extracted by fitting the ellipsometry data with the J.A. Woollam CompleteEASE software.

DFB fabrication
A positive resist (SML 300, EM resist LTD, Macclesfield, UK), was spun (2000 rpm) onto a 15x15 mm silicon chip with a 1.5 µm wet oxide layer yielding a 300 nm thick resist film. The resist was prebaked for 10 min at 180°C. Following the prebake of the resist, a conductive polymer was spun (4000 rpm) onto the sample and prebaked for 2 min at 120°C. Afterwards the sample was exposed at 50 kV in an EBL system (Voyager, Raith GmbH, Dortmund, Germany) with a dose of 750 µC cm -2 . The sample was developed under mild ultrasonication in a solution of isopropanol/H 2 O:7/3 for 45s and descummed for 20s in an O 2 plasma (Pico, Diener, Elbhausen, Germany). The film was then structured in an Inductively Coupled Plasma-
The 2D simulations were carried out in a 10x20 µm area, where the perovskite (n=2.5) was sandwiched between a SiO 2 (n=1.45) layer and vacuum (n=1). At the SiO 2 /perovskite interface there was a square modulation of equal spacing (duty cycle =0.5). A second order scattering boundary condition formed the edges of the simulation to supress back reflection of light. A dipole source (line current) was placed at the centre of the perovskite layer. The dipole oscillated normal to the simulation plane (TE -polarisation) and its frequency was changed from 410 THz to 490 THz with a 0.2 THz step size. During the simulation the field intensity was integrated over a 2 µm long stripe along the perovskite layer with the dipole at its centre.
The resonance frequency of the grating could then be retrieved from the recorded spectrum.
The mesh size of the grating and the perovskite layer was restricted between 5 -50 nm and was determined by the software. Figure S1. a) Thin film X-Ray diffraction (XRD) of the perovskites. A single diffraction peak for each material is visible due to the strong preferential orientation on the substrate. The peak positions are in good agreement with the expected increase in interplanar spacing increasing the size of the templating cation. Temperature dependent XRD measurements and the observed peak shift for each material due to lattice contraction are shown for b) BA 2 SnI 4 , c) PEA 2 SnI 4 and d) NMA 2 SnI 4 . e) Expansion of lattice planes (l) versus temperature for the three perovskites. The linear fit of the experimental data yields a thermal expansion coefficient in the α = dl l • dT direction orthogonal to the perovskite planes of (BA 2 SnI 4 , high = 154 • 10 -6 -1 temperature phase), (BA 2 SnI 4 , low temperature phase), = 102 • 10 -6 -1 = 94 • (PEA 2 SnI 4 ), (NMA 2 SnI 4 ). f) Histogram plot of the linear 10 -6 -1 = 92 • 10 -6 -1 thermal expansion coefficients in the direction normal to the perovskite planes, as extracted from the XRD thermal dependence analysis. The data for CsPbBr 3 are also plotted for comparison (taken from M. S. Kirschner et al, Nat. Commun. 2019, 10, 504).   Figure S4. ASE stability of PEA 2 SnI 4 and NMA 2 SnI 4 under continuous exposure to a 532 nm picosecond laser (pulse duration 800 ps, repetition rate 1KHz) at 284 µJ/cm 2 . Figure S5. PL stability of NMA 2 SnI 4 under continuous exposure to a 532 nm picosecond laser (pulse duration 800 ps, repetition rate 10KHz) at 204 µJ/cm 2 . Figure S6. PL stability of PEA 2 SnI 4 under continuous exposure to a 532 nm picosecond laser (pulse duration 800 ps, repetition rate 10KHz) at 204 µJ/cm 2 . Figure S7. PL stability of NMA 2 SnI 4 resulting from a periodic exposure pattern consisting of periods with and without illumination, each lasting about 5 seconds. The excitation was a 532 nm picosecond laser (pulse duration 800 ps, repetition rate 10KHz) at 204 µJ/cm 2 . Figure S8. Absorbance of PEA 2 SnI 4 for different exposure times (0,15,30 and 90 seconds). s Figure S9. ASE evolution at different temperature for PEA 2 SnI 4 (excitation wavelength 532 nm, pulse duration 800 ps, repetition rate 1 KHz).    Intensity (arb. units) Figure S15. Spectra of the bare PEA 2 SnI 4 film (yellow), PEA-DFB device with a periodicity of 320 nm (green), and PEA-DFB device with a periodicity of 330 nm (purple). All spectra were obtained at room temperature with a pump fluence of 1 mJ/cm 2 .